US-North Korea talks being arranged: Trump

US President Donald Trump says the summit with North Korea's Kim Jong Un is being arranged

US President Donald Trump says he had "a long and very good talk" with the South Korean president after his historic meeting with North Korea's leader.

With anticipation growing for a possible US-North Korea summit, Trump tweeted that "things are going very well", with the "time and location" of a meeting with Kim Jong Un still being set.

The call lasted 75 minutes, according to a statement from the South Korean president's office quoted by the news agency Yonhap.

Trump said he also spoke by phone with Japanese Prime Minister Shinzo Abe "to inform him of the ongoing negotiations", and the Pentagon said US Secretary of Defense James Mattis spoke with South Korean Defence Minister Song Young-moo.

Moon and Kim have pledged to seek a formal end to the Korean War by the end of the year and to rid the Korean Peninsula of nuclear weapons.

Trump has said he is looking forward to the meeting with Kim and it "should be quite something".

It is tentatively scheduled for May or early June.

Earlier, the US president claimed credit for the historic meeting between the leaders of North and South Korea and declared that peace on the divided peninsula could be achieved.

He spoke hours after Kim became the first North Korean leader to travel south of the demarcation line between the two Koreas, meeting Moon.

Responsibility for turning a bold vision for peace into reality will in large part rest with Trump, who has often vowed to succeed where his predecessors have failed in eliminating the North Korean nuclear threat to America.

Earlier, he touted the outcome of Friday's summit between Kim and Moon as a breakthrough in the generational stand-off.

"KOREAN WAR TO END!" he tweeted. "The United States, and all of its GREAT people, should be very proud of what is now taking place in Korea!"

In a separate tweet, he said "good things are happening, but only time will tell".

Mattis and Song said they were committed to "a diplomatic resolution that achieves complete, verifiable and irreversible denuclearisation" of the North, according to the Pentagon's chief spokeswoman, Dana W. White. Mattis also reaffirmed "the ironclad US commitment" to defend its ally "using the full spectrum of US capabilities".